Synthesis of the Optimal RSSR Mechanism for the Motion Transmission Between Skew Axes with Variable Pose

This paper deals with the synthesis of the RSSR mechanism, which is a spatial linkage with two revolute (R) and two spherical (S) kinematic pairs, typically used to transmit rotational motion between shafts with skew axes. The RSSR dimensional synthesis problems for optimal rotatability and/or optimal motion and force transmission have been extensively studied and different procedures were proposed in the literature. A problem of practical interest is the synthesis of the optimal RSSR mechanism for a set of frame links with different geometry of the frame link, i.e. for a given set of relative poses (position and orientation) of the skew shafts, in order to obtain the optimal transmission of motion. This paper presents an original optimization procedure to solve the above mentioned problem. As an example of application a dimensional synthesis of an RSSR mechanism is reported, to provide the optimal force transmission for a given set of the relative pose of the two shafts to drive a mechanism for the thumb motion in a hand exoskeleton. Results are reported that show the effectiveness of the proposed optimization procedure.